Exponential stabilization for Timoshenko beam with different delays in the boundary control

Liu, Xiu Fang; Xu, Genqi

doi:10.1093/imamci/dnv036

Cited by 4 publications

(2 citation statements)

References 13 publications

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“…The similar results for other systems can also be seen in [28,32,34]. Slight later, Shang and Liu et al [17,18,29] extended such dynamic feedback controller design from the difference-type control to more complicated cases that include multi-delay-time and the integral term. Since the dynamic feedback controller design is based on full state of the system, Han et al [12] studied output-based stabilization for an Euler-Bernoulli beam with timedelay in boundary input.…”

Section: Xiaorui Wang and Genqi Xusupporting

confidence: 62%

Uniform stabilization of a wave equation with partial Dirichlet delayed control

Wang¹,

Xu²

2020

Evolution Equations &Amp; Control Theory

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In this paper, we consider the uniform stabilization of some highdimensional wave equations with partial Dirichlet delayed control. Herein we design a parameterization feedback controller to stabilize the system. This is a new approach of controller design which overcomes the difficulty in stability analysis of the closed-loop system. The detailed procedure is as follows: At first we rewrite the system with partial Dirichlet delayed control into an equivalence cascaded system of a transport equation and a wave equation, and then we construct an exponentially stable target system; Further, we give the form of the parameterization feedback controller. To stabilize the system under consideration, we choose some appropriate kernel functions and define a bounded inverse linear transformation such that the closed-loop system is equivalent to the target system. Finally, we obtain the stability of closed-loop system by the stability of target system.

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Section: Xiaorui Wang and Genqi Xusupporting

confidence: 62%

Uniform stabilization of a wave equation with partial Dirichlet delayed control

Wang¹,

Xu²

2020

Evolution Equations &Amp; Control Theory

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show abstract

“…The papers [26,27] extend the dynamic control design to the case that includes distributed delay. [28] considered the multi-time delay case for Timoshenko beam using the dynamic feedback controller. Although the dynamic controller designs have settled the stabilization problem of the system with delay, the stability analysis of resulted closed-loop systems become a difficult work.…”

Section: Introductionmentioning

confidence: 99%

Solvability of the Nonlocal Initial Value Problem and Application to Design of Controller for Heat-Equation with Delay

Xu¹

2019

JMS

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In this paper, we study the solvability of a distribution-valued heat equation with nonlocal initial condition. Under proper assumption on parameters we get the explicit solution of the distribution-valued heat equation. As an application, we further consider the stabilization problem of heat equation with partial-delay in internal control. By the parameterization design of feedback controller, we show if the integral kernel functions are determined by the solution of the distribution heat equation with nonlocal initial value problem, then the closed-loop system can be transformed into a system which is called the target system of the exponential stability under the bounded linear transformation. By selecting different distribution-valued kernel functions, we give the inverse transformation. Hence the closed-loop system is equivalent to the target system.

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Uniform stabilization of 1-d wave equation with anti-damping and delayed control

Zhang

Chen

2020

Journal of the Franklin Institute

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Exponential stabilization for Timoshenko beam with different delays in the boundary control

Cited by 4 publications

References 13 publications

Uniform stabilization of a wave equation with partial Dirichlet delayed control

Uniform stabilization of a wave equation with partial Dirichlet delayed control

Solvability of the Nonlocal Initial Value Problem and Application to Design of Controller for Heat-Equation with Delay

Uniform stabilization of 1-d wave equation with anti-damping and delayed control

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